HSC Science (Computer Science) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Prove the following:

tan A + 2 tan 2A + 4 tan 4A + 8 cot 8A = cot A

Prove the following:

`tan^3x/(1 + tan^2x) + cot^3x/(1 + cot^2x)` = secx cosecx − 2sinx cosx 

Find the value of determinant : 

`|(2, -4),(7, -15)|`

Find the value of determinant :

`|(2"i", 3),(4, -"i")|`

Find the value of determinant :

`|(3, -4, 5),(1, 1, -2),(2, 3, 1)|`

Find the value of determinant :

`|("a", "h", "g"),("h", "b", "f"),("g", "f", "c")|`

Find the value of x if

`|(x^2 - x + 1, x + 1),(x + 1, x + 1)|` = 0

Find the value of x if `|(x, -1, 2),(2x, 1, -3),(3, -4, 5)|` = 29 

Find x and y if `|(4"i", "i"^3, 2"i"),(1, 3"i"^2, 4),(5, -3, "i")|` = x + iy where i² = – 1

Answer the following question:

Evaluate `|(2, -5, 7),(5, 2, 1),(9, 0, 2)|`

Answer the following question:

Evaluate `|(1, -3, 12),(0, 2, -4),(9, 7, 2)|`

Answer the following question:

Find the value of x if

`|(1, 4, 20),(1, -2, -5),(1, 2x, 5x^2)|` = 0

Answer the following question:

Find the value of x if

`|(1, 2x, 4x),(1, 4, 16),(1, 1, 1)| = 0`

If A(1, 3) and B(2, 1) are points, find the equation of the locus of point P such that PA = PB.

A(−5, 2) and B(4, 1). Find the equation of the locus of point P, which is equidistant from A and B

If A(2, 0) and B(0, 3) are two points, find the equation of the locus of point P such that AP = 2BP.

If A(4, 1) and B(5, 4), find the equation of the locus of point P if PA² = 3PB² 

A(2, 4) and B(5, 8), find the equation of the locus of point P such that PA² − PB² = 13

A(1, 6) and B(3, 5), find the equation of the locus of point P such that segment AB subtends right angle at P. (∠APB = 90°)

If the origin is shifted to the point O′(2, 3), the axes remaining parallel to the original axes, find the new co-ordinates of the point A(1, 3)